The following chart displays two variables: the percent changes from the previous year of Unit Labor Cost (ULC) and Personal Consumption Expenditures: Chain-type price Index (PCE). The movements of two series had been very close to each other before the financial crisis, but two series diverged after the financial crisis. (see in red circle) the ULC began to rise lately while the PCE was declining.

The following chart is the scatter chart which displays the relationship between two variables (ULC and PCE). The blue line represents the relationship between two variables for the entire period (from 1970 to 2016) which shows the positive relationship. However, the red line represents the relationship between two variables after the financial crisis (2007-2008) and there is almost no relationship between them. So, the relationship is broken after the financial crisis.

The regression model (PCE (inflation) = a*UCL+b) for the entire period is valid.

The following chart shows the comparison of two regression models: One represents the blue line and the other represents the red line.

The following chart displays the two data ; actual PCE vs predicted PCE. the predicted values by the model were close to the actual PCE before the financial crisis, but the predicted values by the model after the financial crisis were way off from the actual values (in red circle).

The following chart shows the residual line (Actual PCE – Predicted PCE). If the model predicts well, then the line should stay near zero. The residual line stayed near zero before the financial crisis, but the line stayed fell away from zero. However, it started to climb to the zero.